Patents:
U.S. Pat. No. 5,838,561 Automatic control loop monitoring and diagnostics
U.S. Pat. No. 5,796,606 Process information system for distributed control systems
U.S. Pat. No. 6,208,949 Method and apparatus for dynamical system analysis
This invention relates to a technique to accurately assess the performance of Model Predictive Controllers. Specifically, the technique accounts for the known disturbance model of the controller in assessing the controller performance.
Model Predictive Controllers (also termed Dynamic Matrix Controllers, Multi-Variable Controllers, etc.) are widespread in industry and account for significant economic benefits. It is necessary to evaluate the performance of these controllers for the following reasons:
1. Evaluate current benefits of the Model Predictive Controller (MPC) application.
2. Explore future control opportunities.
3. Analyze current controller shortcomings.
Performance is largely defined it two ways: 1) How well does the controller maintain the process measurement at setpoint; and 2) How effectively does the controller determine the optimum operating conditions. Methods for evaluating the first question are the subject of this patent.
The simplest and most direct technique of determining controller performance is to calculate the variance between the measurement (PV) and the setpoint (SP), i.e.,       σ    2    =            1      n        ⁢                  ∑                  i          =          1                n            ⁢              xe2x80x83            ⁢                        (                      PV            -            SP                    )                2            
While simple to calculate, this measure has the extreme disadvantage that it is dependent on the level of disturbances or setpoint changes (i.e., the only reason why the SP would not equal the PV is due to disturbance/setpoint changes), and is thus more an indication of the disturbance/setpoint spectrums than the capabilities of the controller.
For this reason Harris et al. (1992) (Harris, T., and Desborough, L., Performance Assessment Measures for Univariate Feedback Control, Cdn J. of Chem. Eng., 70, pp 1186-1197, 1992) defined a Performance Index measure (xcex7) that is independent of the disturbance/setpoint change spectrum and can be readily used to determine the actual performance of the controller. This measure compares the performance of the controller to a theoretical Minimum Variance controller (i.e., the best physically realizable linear controller), and can be calculated from routine operating data. This latter property is a strong advantage, as no plant tests are required to determine the measure. This measure is common in industry and is often referred to as the Harris Performance Index. This technology described in this patent is a modification or extension to the Harris Performance Index to account for one of the limitations of Model Predictive Controllers.
The Minimum Variance controller referenced by Harris (1992) employs an open-loop model of the process in the following form:                               y          t                =                                                                              ω                  ⁡                                      (                    B                    )                                                  ⁢                                  B                  b                                                            δ                ⁡                                  (                  B                  )                                                      ⁢                          u              t                                +                                                    θ                ⁡                                  (                  B                  )                                                                              φ                  ⁡                                      (                    B                    )                                                  ⁢                                  ∇                  d                                                      ⁢                          a              t                                                          (        1        )            
This is standard time series notation for process transfer functions, and says that the output yt is a function of the input ut and an independent white noise input at. The input passes through a linear discrete process model, while the noise input passes through a linear discrete disturbance model Some model predictive controllers use a slightly different formulation of the process model, but the results are invariant to this different formulation.
The minimum variance controller requires full specification of the disturbance model (the second term on the right hand side (RHS) of equation 1). In contrast, the majority of model predictive controllers (MPC) use the following model in their design:                               y          t                =                                                                              ω                  ⁡                                      (                    B                    )                                                  ⁢                                  B                  b                                                            δ                ⁡                                  (                  B                  )                                                      ⁢                          u              t                                +                                    1              ∇                        ⁢                          a              t                                                          (        2        )            
Note the simplified disturbance model term. The reason for this simplified model is that it does not require parameter identification from plant tests (generally very difficult as the input sequence at is by definition unscheduled and unmeasured), and this form of the disturbance model results in robust control.
This is problematic for the Harris Performance Index. The actual disturbance entering the process is often more accurately of the form:                               n          t                =                                            (                              1                -                                                      θ                    1                                    ⁢                  B                                            )                                                      (                                  1                  -                                                            φ                      1                                        ⁢                    B                                                  )                            ∇                                ⁢                      a            t                                              (        3        )            
For processes under MPC control and with the above disturbance entering the process, the Harris Performance Index will indicate poor control, even if the process model is exact and there are no restrictions in the input movement. While this is correct (the MPC controller is in fact sluggish under these circumstances compared to a minimum variance controller), it is of not much use to the practicing control engineer.
This is because the control engineer needs to determine if the sluggishness is a result of the two factors under his control, namely controller tuning and model fidelity. The control engineer has no control over the structure of the disturbance model in the controller. As the Harris Performance Index does not differentiate between the causes of poor control, the Harris Performance Index can be of limited use, or even misleading.
While the minimum variance controller used as a reference controller by Harris et al., requires specification of a full open-loop process and disturbance model, an estimate of the performance of a minimum variance controller does not require specifying or determining any process or disturbance model. In contrast, while a Model Predictive Controller does not require specifying a disturbance model, determining the performance of a Model Predictive Controller does require that the disturbance model be specified.
There are other less sophisticated performance measurements used by industry. A common one is an autocorrelation graph of the controller errors (i.e., PV-SP), but this suffers from the same deficiency as the Harris Performance Index. A disturbance of the form of Equation 3 will result in significant autocorrelation even if the process transfer function is perfect and there are no input move restrictions.
Of concern in the present invention is to determine the performance of Model Predictive Controllers using normal closed-loop operating data Also of concern in the present invention is for the performance measure to reflect the structure of assumed disturbance model in the MPC controller.
It is, therefore, a feature of the present invention to provide a method to determine the performance of a Model Predictive Controller.
It is, also, a feature of the present invention that it only requires normal operating data to determine the controller performance.
Yet another feature of the present invention is that the performance measure adequately reflects the structure of the assumed disturbance model in the Model Predictive Controller.
It is, also, a feature of the present invention that it has the same range and interpretation as the Harris Controller Performance Index.
Additional features and advantages of the invention will be set forth in part in the description which follows, and will in part be apparent from the description, or may be learned from practice of the invention. The features and advantages of the invention may be realized by means of the combinations and steps pointed out in the appended claims.
To achieve the objectives, features, and advantages, in accordance with the purpose of the invention as embodied and broadly described herein, a method to determine the performance of a Model Predictive Controller is provided. This performance measure accounts for the fixed disturbance model of Model Predictive Controllers and may be calculated using only on-line data.
Accordingly, besides the objects and advantages of the Model Predictive Controller Performance Index described above, several objects and advantages of the present invention are:
a) to assess the performance of a Model Predictive controller using only normal operating data;
b) to obtain a measure that has the same interpretation and range of the Harris controller performance index;
c) to obtain a measure that accounts for the fixed disturbance model structure of the controller;
d) to obtain a measure that is not indicative of the actual disturbance model of the process, but indicates the process model fidelity and tuning of the controller;
e) to estimate disturbance model parameters using only closed-loop data and an estimate of the deadtime.